Constructing tilted algebras from cluster-tilted algebras

Co-authored with Steffen Oppermann and Anette Wrålsen.

Any cluster-tilted algebra is the relation extension of a tilted algebra. We present a method to, given a cluster-tilting object, construct all tilted algebras whose relation extension is the endomorphism ring of this cluster-tilting object. Furthermore, in the Dynkin case, we provide a technique to find a cluster-tilting object, having a given cluster-tilted algebra as endomorphism ring.